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286 . $x^{2} + y^{2} + x^{2} = 5, x + y + z = 3$ হলে yz + zx -xy এর মান কত?

A. -5
B. -4
C. -3
D. -2

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Answer: Option D

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287 . $a^{4} - 51 a^{2} + 1 = 0$ হলে $a - \frac{1}{a}$ এর মান কত?

A. $\pm 9$
B. $\pm 7$
C. $\pm 5$
D. $\pm 3$

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Answer: Option B

Explanation:

দেওয়া আছে, a^{4} - 51 a^{2} + 1 = 0 \Rightarrow a^{4} + 1 = 51 a^{2} \Rightarrow \frac{a^{4} + 1}{a^{2}} = \frac{51 a^{2}}{a^{2}} \Rightarrow \frac{a^{4}}{a^{2}} + \frac{1}{a^{2}} = 51 \Rightarrow a^{2} + \frac{1}{a^{2}} = 51 এখন, {(a - \frac{1}{a})}^{2} = {(a + \frac{1}{a})}^{2} - 4 . a . \frac{1}{a} = a^{2} + 2 . a . \frac{1}{a} + \frac{1}{a^{2}} - 4 = a^{2} + \frac{1}{a^{2}} - 2 = 51 - 2 = 49 ∴ a - \frac{1}{a} = \sqrt{49} = \pm 7

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288 . $4 x^{2} - 2$ হতে কত বিয়োগ করলে রাশিটি পূর্ণবর্গ হবে?

A. $- \frac{1}{4 x^{2}}$
B. $- \frac{1}{2 x^{2}}$
C. $\frac{1}{4 x^{2}}$
D. $\frac{1}{2 x^{2}}$

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Answer: Option A

Explanation:

4 x^{2} - 2 = {(2 x)}^{2} - 2.2 x . \frac{1}{2 x} + {(\frac{1}{2 x})}^{2} - {(\frac{1}{2 x})}^{2} = {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} {সুতরাং, 4x}^{2} -2 হতে - \frac{1}{4 x^{2}} বিয়োগ করলে রাশিটি পূর্ণবর্গ হবে। {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} - (- \frac{1}{4 x^{2}}) = {(2 x - \frac{1}{2 x})}^{2} - \frac{1}{4 x^{2}} + \frac{1}{4 x^{2}} = {(2 x - \frac{1}{2 x})}^{2}

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289 . $\frac{a^{3} - b^{3}}{a + b}$ কে $\frac{a^{4} + b^{4} + a^{2} b^{2}}{a^{3} + b^{3}}$ দ্বারা ভাগ করলে ভাগফল কত হবে?

A. $a - b$
B. $a + b$
C. $a^{2} - b^{2}$
D. $a^{2} + b^{2}$

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Answer: Option A

Explanation:

\frac{a^{3} - b^{3}}{a + b} \div \frac{a^{4} + b^{4} + a^{2} b^{2}}{a^{3} + b^{3}} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \div \frac{{(a^{2})}^{2} + 2 . a^{2} . b^{2} + {(b^{2})}^{2} - {(a b)}^{2}}{(a + b) (a^{2} - a b + b^{2})} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \times \frac{(a + b) (a^{2} - a b + b^{2})}{{(a^{2} + b^{2})}^{2} - {(a b)}^{2}} = \frac{(a - b) (a^{2} + a b + b^{2})}{a + b} \times \frac{(a + b) (a^{2} - a b + b^{2})}{(a^{2} + b^{2} + a b) (a^{2} + b^{2} - a b)} = (a - b)

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290 . $x^{2} - 4 x + 1 = 0$ হলে $x \div (x^{2} - 3 x + 1)$ এর মান কত?

B. 1
C. 2
D. 4

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Answer: Option B

Explanation:

x² - 4x + 1 = 0

বা, x² + 1 = 4x

x/( x² - 3x + 1)

বা, x / 4x - 3x

∴x/x = 1

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বাংলাদেশ পাবলিক সার্ভিস কমিশন (BPSC) || জুনিয়র ইন্সট্রাক্টর (18-03-2023) ||

291 . $\frac{x}{y} + \frac{y}{x} = 6$ হলে $\frac{x^{2}}{y^{2}} + \frac{y^{2}}{x^{2}}$ এর মান কত?

A. 30
B. 32
C. 34
D. 36

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Answer: Option C

Explanation:

{(x/y) + (y + x)}² = 6²

= > (x²/y²) + 2.(x/y).(y/x) + (y²/x²) = 6²

= > (x²/y²) + (y²/x²) = 36 - 2 = 34

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292 . $x + \frac{1}{x} = 3$ হলে $x^{3} + \frac{1}{x^{3}}$ এর মান কত?

A. 16
B. 18
C. 22
D. 1

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Answer: Option B

Explanation:

দেওয়া আছে, x + \frac{1}{x} = 3 এখন, x^{3} + \frac{1}{x^{3}} = {(x + \frac{1}{x})}^{3} - 3 . x . \frac{1}{x} (x + \frac{1}{x}) = 3^{3} - 3.3 = 27 - 9 = 18

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অর্থ মন্ত্রণালয়ের অফিস সহকারী-০৬.০৫.২০১১

293 . x+y=8, xy==15 হলে ${(x - y)}^{4} = ?$

A. 4
B. 8
C. 9
D. 16

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Answer: Option D

Explanation:

আমরা জানি, {(x - y)}^{2} = {(x + y)}^{2} - 4 x y = 8^{2} - 4 \times 15 = 64 - 60 = 4 ∴ x - y = 2 ∴ (x + y) + (x - y) = 8 + 2 \Rightarrow 2 x = 10 ∴ x = 5 ∴ y = 8 - 5 = 3 ∴ {(x - y)}^{4} = {(5 - 3)}^{4} = 2^{4} = 16

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294 . $p^{2} - 4 p + 1 = 0$ সমীকরণের মূলদ্বয় ‍a ও B হলে a + B ও aB মূলবিশিষ্ট সমীকরণ কোনটি?

A. $p^{2} - 4 p + 5 = 0$
B. $p^{2} + 5 p - 4 = 0$
C. $p^{2} + 4 p - 5 = 0$
D. $p^{2} - 5 p + 4 = 0$

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Answer: Option D

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295 . $x^{2} - 3 x + 2 = 0$ সমীকরণের মূল দুটি হবে -

A. অবাস্তব ও অসমান
B. বাস্তব ও সমান
C. বাস্তব ও অসমান
D. বাস্তব ও অমূলদ

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Answer: Option C

Explanation:

x^{2} - 3 x + 2 = 0 \Rightarrow x^{2} - 2 x - x + 2 = 0 \Rightarrow x (x - 2) - 1 (x - 2) = 0 \Rightarrow (x - 1) (x - 2) = 0 ∴ x - 1 = 0 x = 1 A g a i n, x - 2 = 0 x = 2 সুতরাং, সমীকরনের মূলদ্বয় অসমান ও বাস্তব।

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বাংলাদেশ পাবলিক সার্ভিস কমিশন -২০১৯ পদের নাম : বিভিন্ন মন্ত্রণালয়ের ব্যক্তিগত কর্মকর্তা ( ১৩. ০৯.২০১৯ )

296 . $x^{2} - x - 2$ এর একটি উৎপাদক -

A. (x +1)
B. (x +2)
C. (x-3)
D. (x-1)

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Answer: Option A

Explanation:

x^{2} - x - 2 = x^{2} - 2 x + x - 2 = x (x - 2) + 1 (x - 2) = (x + 1) (x - 2)

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297 . $x^{2} + 7 x + 12 = 0$ সমীকরণটির উৎপাদক _

A. (x+3)(x+4)
B. (x+3)(x-4)
C. (x-3)(x+4)
D. (x-3)(x-4)

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Answer: Option A

Explanation:

x^{2} + 7 x + 12 = x^{2} + 4 x + 3 x + 12 = x (x + 4) + 3 (x + 4) = (x + 3) (x + 4)

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প্রতিরক্ষা মন্ত্রণালয়ের মিলিটারি ইঞ্জিনিয়ার সার্ভিসেস | স্টোরম্যান | ১৮.০৫.২০১৮

298 . $9 x^{2} - 9 x - 4$ এর উৎপাদক কোনটি?

A. (3x +1) (3x +4)
B. (3 + x ) ( 3x -4)
C. (3x + 1 ) (3x -4)
D. (3x +1) (4x +3)3

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Answer: Option C

Explanation:

9 x^{2} - 9 x - 4 = 9 x^{2} - 12 x + 3 x - 4 = 3 x (3 x - 4) + 1 (3 x - 4) = (3 x + 1) (3 x - 4)

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পরিবার পরিকল্পনা অধিদপ্তর ।। পরিবার কল্যাণ পরিদর্শিকা (18-02-2023)

299 . কোন দুটি $x^{2} - x - 6 = 0$ সমীকরণের মূল ?

A. 2,3
B. 2,-3
C. -2,3
D. -2,-3

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Answer: Option C

Explanation:

x^{2} - x - 6 = 0 \Rightarrow x^{2} - 3 x + 2 x - 6 = 0 \Rightarrow x (x - 3) + 2 (x - 3) = 0 \Rightarrow (x + 2) (x - 3) = 0 S o, x = 3 o r, x = - 2

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স্থানীয় সরকার বিভাগের অধীন | জনস্বাস্থ্য প্রকৌশল অধিদপ্তরের | এস্টিমেটর | ০২.০২.২০১৮

300 . x =5 এবং y=2 হলে $16 x^{2} - 56 x y + 49 y^{2}$ এর মান কত?

A. 204
B. 1156
C. 36
D. 6

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Answer: Option C

Explanation:

16x² - 56xy + 49y²

= (4x)² – 2.4x.7y + (7y)²

= (4x - 7y)²

= (4.5 - 7.2)²

= (20 - 14)²

= (6)²

= 36.

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স্বাস্থ্য মন্ত্রণালয় | অফিস সহকারী কাম- কম্পিউটার মুদ্রাক্ষরিক | ১১.০১.২০১৯

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